Relata are the terms that show up in the causal relation. ## deterministic theory of causality A deterministic theory of causality is one that states effect B always follows from cause A. For example, when a billiard ball strikes another, we might say that the first ball caused, deterministically, the second ball to accelerate. We could even use a model like $F = ma$ to describe deterministically what will happen to the second ball just by knowing the characteristics of the first ball. (Interestingly, our current understanding of quantum mechanics would actually suggest that the causality in this case is actually a probabilistic theory of causality. There is some vanishingly small probability that one billiard ball passes entire through the other. This is called the tunneling effect). ## probabilistic theory of causality A probabilistic theory would say that effect B has a higher chance of occurring after cause A occurs. When we say smoking causes cancer, what we really mean is that smoking increases the risk of cancer, or increases the probability that an individual who smokes will develop cancer later. It is not guaranteed, but modern medicine has a mechanistic understanding of how the chemicals in cigarette smoke influence the factors that promote cancer sufficiently to say that there is not some third confounding variable that causes both smoking and cancer in individuals. ## counterfactual theory of causality Under the counterfactual theory of causality, A causes B if, in the absence of A, B would not have occurred or would be less likely to occur. Unfortunately, we can never observe the counterfactual. This leads to the **fundamental problem of causal inference.** Causal effects cannot be measured directly, which is a problem for the scientific method or empiricism. ## structural theory of causality The statement that A causes B can only be evaluated within the context of a structural model that explains why A causes B. ## conditions for establishing causation 1. Empirical association 2. Correct temporal relationship 3. Non-spuriousness (actual cause not just correlatives) ## research design for causal inference A few approaches are possible to overcome the fundamental problem of causal inference. 1. Find close substitutes to observe that represent the counterfactual 2. Randomized experiments 3. Make additional assumptions about the observational data Close substitutes are individuals (or other statistical units) that are the same in all other ways except they took the path of the counterfactual. For example, studies of twins are common in untangling the difference in genes versus environmental factors (nature versus nurture). A study of twins separated at birth where one was raised in a high socio-economic home and one in a lower socio-economic home could help understand the effect of socio-economic status on high school achievement for example. https://plato.stanford.edu/entries/causation-metaphysics/